June 2006 6679 Mechanics M3 Mark Scheme Question Number
Scheme
1.
Use of y 2 dx x xy 2 dx
Marks
x dx x x
2
M1
dx
1 2 1 3 2 x x 3 x 16 64 x 2 3 8 x 3
Using limits 0 and 4
A1 = A1 M1 A1
(5) [5]
2.
(a)
Small Hemisphere Mass ratios
2 a 3 2
x
3 a 16
3
Bowl
2 7a 3 8
Large Hemisphere 3
2 3 a 3 Anything in the ratio 1 : 7 : 8 3 a 8
x
3 3 a 7 x 8 a 16 8 45 Leading to x a 112 1
(b)
Bowl M
Mass Ratios
45 a 112
x
M
Liquid kM
Bowl and Liquid k 1 M
3 a 16
17 a 48
45 3 17 a kM a k 1 M a 112 16 48 2 Leading to k 7
B1
B1
M1 A1 cso
A1
(5)
B1 B1
M1 A1 A1
(5) [10]
1